Fractured reservoirs are an extreme kind of heterogeneous reservoirs, with two contrasted media, a matrix medium containing most of the oil in place and having a low permeability, and a fracture medium usually representing less than 1% of the oil in place and being highly conductive. The fracture medium itself may be complex, with different fracture sets characterized by their respective fracture density, length, orientation, tilt and aperture. 3D images of fractured reservoirs are not directly usable as a reservoir simulation input. Representing the fracture network in reservoir flow simulators was long considered as unrealistic because the network configuration is partially unknown and because of the numerical limitations linked to the juxtaposition of numerous cells with extremely-contrasted size and properties. Hence, a simplified but realistic modeling of such media remains a concern for reservoir engineers.
The "dual-porosity approach" as taught for example by Warren, J. E. et al "The Behavior of Naturally Fractured Reservoirs", SPE Journal (September 1963), 245-255, is well-known in the art to interpret the single-phase flow behavior observed when testing a fractured reservoir. According to this basic model, any elementary volume of the fractured reservoir is modeled as an array of identical parallelepipedic blocks limited by an orthogonal system of continuous uniform fractures oriented along one of the three main directions of flow. Fluid flow at the reservoir scale occurs through the fracture medium only and locally fluid exchanges occur between fractures and matrix blocks.
Numerous fractured reservoir simulators have been developed using such a model with specific improvements concerning the modeling of matrix-fracture flow exchanges governed by capillary, gravitational, viscous forces and compositional mechanisms, also the consideration of matrix to matrix flow exchanges (dual permeability dual-porosity simulators). Various examples of prior art techniques are referred to in the following references.
Thomas, L. K. et al: "Fractured Reservoir Simulation," SPE Journal (February 1983) 42-54; PA1 Quandalle, P et al: "Typical Features of a New Multipurpose Reservoir Simulator", SPE 16007 presented at the 9th SPE Symposium on Reservoir Simulation held in San Antonio, Tex., Feb. 1-4, 1987; PA1 Coats, K. H.: "Implicit Compositional Simulation of Single-Porosity and Dual-Porosity Reservoirs," paper SPE 18427 presented at the SPE Symposium on Reservoir Simulation held in Houston, Tex., Feb. 6-8, 1989. PA1 Odling, N. E.: "Permeability of Natural and Simulated Fracture Patterns," Structural and Tectonic Modelling and its Application to Petroleum Geology NPF Special Publication 1, 365-380, Elsevier. Norwegian Petroleum Society (NPF) 1992; PA1 Long, J. C. S., et al; "A Model for Steady Fluid Flow in Random Three-Dimensional Networks of Disc-Shaped Fractures," Water Resources Research (August 1985) vol. 21, No. 8, 1105-1115; PA1 Cacas, M. C. et al; "Modeling Fracture Flow With a Stochastic Discrete Fracture Network: Calibration and Validation. 1. The Flow Model," Water Resources Research (March 1990) vol. 26, No. 3; PA1 Billaux, D.: &lt;&lt;Hydrogeologie des milieux fractures. Geometrie, connectivite et comportement hydraulique&gt;&gt; PhD Thesis, presented at the Ecole Nationale Superieure des Mines de paris; Document du BRGM N.degree.186, Editions du BRGM, 1990; PA1 Robinson, P. C.: &lt;&lt;Connectivity, Flow and Transport in networks Models of Fractured Media&gt;&gt;, PhD Thesis, St Catherine's College, Oxford University, Ref.: TP1072, May 1984. PA1 discretizing the fracture network in fracture elements (such as rectangles for example) and defining nodes representing interconnected fracture elements in each layer of the medium; and PA1 determining fluid flows through the discretized network while imposing boundary pressure conditions, and fluid transmissivities to each couple of neighboring nodes. PA1 partitioning the medium in a set of parallel layers each extending in a reference plane perpendicular to a reference axis and defined each by a co-ordinate along said axis; PA1 partitioning each fracture in a series of rectangles limited along said reference axis by two adjacent layers and itemizing the rectangles by associating therewith geometrical and physical attributes such as co-ordinates and sizes of the rectangles and hydraulic conductivities of the fractures; PA1 positioning nodes in each layer for all the interconnected fractures; and PA1 for all the couples of neighboring nodes, calculating transmissivity factors and solving flow equations to determine the equivalent permeabilities of the medium in three orthogonal directions.
A problem met by reservoir engineers is to parameterize this basic model in order to obtain reliable flow predictions. In particular, the basic fracture and matrix petrophysical properties as well as the size of matrix blocks have to be known for each cell of the flow simulator. Whereas matrix permeability can be estimated from cores, the permeability of the fracture network contained in the cell, i.e. the equivalent fracture permeability, cannot be estimated in a simple way and requires taking the geometry and properties of the actual fracture network into account.
A direct method is known for determining steady-state flow in a fracture network. It involves use of conventional fine regular grids discretizing both the fractures and the matrix blocks of the parallelepipedic fractured rock volume considered. For several reasons this known method does not provide reliable results except if the fractured rock volume is discretized using a grid with a drastically-high number of cells, which requires huge computing ressources.
Other specific models which compute equivalent permeabilities of 2D or 3D fracture networks, are also known for example from: